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Posted 2015-02-18, 05:56 PM in reply to Goodlookinguy's post starting "Can you be more explicit. A blanket..."
Goodlookinguy said: [Goto]
Can you be more explicit. A blanket statement saying that "many" were developed without any forethought is really wrong sounding. As "many" were developed for real-world application. Having relationships to more advanced formulas is no coincidence. You should go read up on the history of math.
Sure, I can be more specific. A few examples:
  • Conic sections were studied purely for their mathematical properties by the ancient Greeks almost 2000 years before they found an application in celestial mechanics
  • Non-Euclidean geometry when studied by Riemann was considered to be mental masturbation until Einstein used it in General Relativity
  • Euler's constant was studied as a problem of compounding interest until it found a use in nuclear decay
  • The distribution of prime numbers has interested mathematicians for centuries, but only relatively recently found application in cryptography.

Even the famous physicist David Hilbert was astounded by the fact that math was almost unbelievably applicable to the real world. In fact, he was astounded by how this fact applied to even his own work: "I developed my theory of infinitely many variables from purely mathematical interests and even called it 'spectral analysis' without any pressentiment that it would later find an application to the actual spectrum of physics."

It seems to me that much of the mathematical development, especially of the previous two centuries, has occurred without consideration for real world application.
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